What really stuck me about these two were the similarities between them. On the surface, both films are about a King Henry of England (in Becket, its Henry II as played by a magnificent Peter O'Toole, while A Man for All Seasons concerns Henry VIII, played by scenery-chewer Robert Shaw) struggling with a religious leader over political affairs (Becket's Richard Burton is Thomas Becket; A Man for All Season's Oscar-winning Paul Scofield is Sir Thomas More). Both were Best Picture nominees, and scored a Best Actor nomination for its leads (though Becket scored nominations for both Burton and O'Toole). I personally find it egregious that Rex Harrison won the 1964 Best Actor prize over O'Toole, Burton, and Dr. Strangelove's Peter Sellars (I have not seen Anthony Quinn in Zorba the Greek); it's one of those travesties that I will never forgive AMPAS for.
But here's the more interesting undercurrent that I've seen between the two films: even though they're two years apart, there's a marked difference in the way they're made. The 1960s were a turbulent time for cinema, as the New Waves brought a fresh new approach to what a film can be and mean. This lead to a unique conflict within the cinematic world. In one corner there were films like Becket, representing the "Old Hollywood" that ran on the studio system and loved royalty dramas, expensive epics, musicals, and light, inoffensive comedies. On the other hand was the "New Hollywood," influenced by the New Waves and explored violence, sex, rebellion, and other previously taboo subjects. The way these films were shot differed; Old Hollywood had a polished, stately look and were shot almost completely on soundstages, whereas New Hollywood would have a gritty, rougher look and often shot on location.
Becket falls squarely in the mode of Old Hollywood. A Man for All Seasons, on the other hand, falls somewhere in between Old and New Hollywood; there's plenty of soundstage-shot traditional melodrama, and the subject matter is no different from what Hollywood loved at the time (1966). And yet there's a touch of New Wave influence to be seen as well, as director Fred Zinneman (who directed High Noon and Old-Hollywood-staple From Here to Eternity) includes loving shots of nature in between expository scenes, an unusual move for such a film. He also gets creative in his staging of the action, making the film slightly rougher around the edges compared to similar films of its day. The New Hollywood was nowhere near being in full-swing yet, but the seeds of change were starting to sprout.
Of course, some things never change. Though the films of today are drastically different in style from the films of half a century ago, the popular genres have not changed. Studios still like to churn out epics (now in the blockbuster action vein) and light comedies (musicals....not so much, though the argument for more is certainly justified), and Oscar still loves a royalty drama, perhaps more than any other genre of film (apart from family dramas and boxing movies, of course).
*By the way, if you want to read a superior account of how New Hollywood was born, I highly recommend Mark Harris' Pictures at a Revolution. Its a phenomenal book.